16. Angular Momentum

A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the top's precession frequency in rpm?

Which of the following expressions correctly gives the angular momentum of a particle of mass $m$ moving with velocity $v$ at a position vector $r$ relative to the origin?

The position of a particle with mass m traveling on a helical path (see Fig. 11–48) is given by $\overrightarrow{r}$ = R cos (2πz/d) î + R sin (2πz/d) ĵ + zk̂ where R and d are the radius and pitch of the helix, respectively, and z has time dependence z = v_𝓏t where v_𝓏 is the (constant) component of velocity in the z direction. Determine the time-dependent angular momentum $\overrightarrow{L}$ of the particle about the origin.

A circular coil of radius $R$ and moment of inertia $I$ is placed in a uniform magnetic field $B$. The coil is free to rotate about its axis, which is perpendicular to the magnetic field. If a current $I$ (current, not moment of inertia) is suddenly started in the coil, what is the initial angular acceleration $\alpha$ of the coil just after the current is started?

Two turbines, A and B, are rotating at constant angular speeds. Turbine A has an angular speed of $\omega =2.0$ rad/s, and turbine B has an angular speed of $\omega =3.0$ rad/s. If both start at the same time, which turbine takes less time to rotate through an angular displacement of $1.0$ radian?

A block of mass $m$ is attached to a light string wound around a solid cylinder of mass $M$ and radius $R$. The cylinder rotates freely about its horizontal axis. When the block is released and descends, what is the magnitude $\alpha$ of the angular acceleration of the cylinder?

A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity ω, then the end of the axle is placed on a support that allows the gyroscope to precess. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

Which of the following best describes the difference between linear momentum and angular momentum?

Which of the following quantities contribute to the angular momentum of a spinning object?

A toy gyroscope consists of a 170-g disk with a radius of 5.5 cm mounted at the center of a thin axle 21 cm long (Fig. 11–42). The gyroscope spins at 45 rev/s. One end of its axle rests on a stand and the other end precesses horizontally about the stand. How long does it take the gyroscope to precess once around?

When solid sphere 4 m in diameter spins around its central axis at 120 RPM, it has 1,000 kg m² / s in angular momentum. Calculate the sphere's mass.

What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? Give your answer using unit vectors.

A composite disc is built from a solid disc and a concentric, thick-walled hoop, as shown below. The inner disc has mass 4 kg and radius 2 m. The outer disc (thick-walled) has mass 5 kg, inner radius 2 m, and outer radius 3 m. The two discs spin together and complete one revolution every 3 s. Calculate the system's angular momentum about its central axis.

A computer disk drive is turned on starting from rest and has constant angular acceleration. Which equation correctly gives the angular displacement $\theta$ after time $t$?

(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? Consult Appendix E and the astronomical data in Appendix F